Adaptive treatment allocation and selection in multi-arm clinical trials: a Bayesian perspective

Background: Adaptive designs offer added flexibility in the execution of clinical trials, including the possibilities of allocating more patients to the treatments that turned out more successful, and early stopping due to either declared success or futility. Commonly applied adaptive designs, such as group sequential methods, are based on the frequentist paradigm and on ideas from statistical significance testing. Interim checks during the trial will have the effect of inflating the Type 1 error rate, or, if this rate is controlled and kept fixed, lowering the power. Results: The purpose of the paper is to demonstrate the usefulness of the Bayesian approach in the design and in the actual running of randomized clinical trials during Phase II and III. This approach is based on comparing the performance of the different treatment arm in terms of the respective joint posterior probabilities evaluated sequentially from the accruing outcome data, and then taking a control action if such posterior probabilities fall below a pre-specified critical threshold value. Two types of actions are considered: treatment allocation, putting on hold at least temporarily further accrual of patients to a treatment arm (Rule 1), and treatment selection, removing an arm from the trial permanently (Rule 2). The main development in the paper is in terms of binary outcomes, but extensions for handling time-to-event data, including data from vaccine trials, are also discussed. The performance of the proposed methodology is tested in extensive simulation experiments, with numerical results and graphical illustrations documented in a Supplement to the main text. As a companion to this paper, an implementation of the methods is provided in the form of a freely available R package. Conclusion: The proposed methods for trial design provide an attractive alternative to their frequentist counterparts.

Comparing Bayesian Statistics and Frequentist Statistics in Serious Games Research

This article presents three empirical studies on the effectiveness of serious games for learning and motivation, while it compares the results arising from Frequentist (classical) Statistics with those from Bayesian Statistics. For a long time it has been technically impracticable to apply Bayesian Statistics and benefit from its conceptual superiority, but the emergence of automated sampling algorithms and user-friendly tools has radically simplified its usage. The three studies include two within-subjects designs and one between-subjects design. Unpaired t-tests, mixed factorial ANOVAs and multiple linear regression are used for the analyses. Overall, the games are found to have clear positive effects on learning and motivation, be it that the results from Bayesian Statistics are more strict and more informative, and possess several conceptual advantages. Accordingly, the paper calls for more emphasis on Bayesian Statistics in serious games research and beyond, as to reduce the present domination by the Frequentist Paradigm.

Classical Statistical Inference

This chapter introduces the main concepts of statistical inference, or drawing conclusions from data. There are three main types of inference: point estimation, confidence estimation, and hypothesis testing. There are two major statistical paradigms which address the statistical inference questions: the classical, or frequentist paradigm, and the Bayesian paradigm. While most of statistics and machine learning is based on the classical paradigm, Bayesian techniques are being embraced by the statistical and scientific communities at an ever-increasing pace. The chapter begins with a short comparison of classical and Bayesian paradigms, and then discusses the three main types of statistical inference from the classical point of view.